The Global Food Price Crisis of 2007-2011 had mixed effects on the poor in developing nations. By some estimates, the Crisis lifted nearly 24 million poor farmers out of poverty; however, it also cast 68 million net food buyers into poverty. In this paper, we analyze the distributional impacts of the Crisis and the merits of different food security policies proposed to address it, focusing on policies that employ buffer stock reserves, direct cash transfers, emergency export bans, and transportation infrastructure enhancements. Of special interest are how the impacts of these policies differ among the rural and urban poor and between importing and exporting countries. Our analysis is based on a stylized stochastic dynamic heterogeneous agent model of a developing country exposed to aggregate food production and world food price risk that is populated by rural and urban poor who suffer from "malnutrition" whenever their resources are insufficient to meet basic nutritional needs.